Based on that equation that appears to accurately chart scores for finished puzzles, the best strategy is to get really good at solving puzzles in the 600-700 second range. These puzzles are short enough to get really good times and scores. When trying to solve short 4X4 puzzles, I only get around 330 points even if I set a new record for it.

As for getting faster, it still comes down to practice. I've improved markedly even after I thought I was really good. There are plateaus that can persist for a while before progress is seen.